Table of contents

December 2003 marks the end of an era in the world of metrology with the retirement of Terry Quinn FRS, Director of the BIPM since 1988. Terry's contribution to the field of metrology has been long and distinguished, both as a physicist and administrator; a long list of awards and honours bears testimony to the fact.

From the standpoint of physics, his contributions have been numerous and important: in the field of thermometry he pioneered the use of cryogenic radiometers, instruments that are now employed as standards by National Metrology Institutes (NMIs) worldwide; his experiments to measure the Newtonian gravitational constant, G, the least well known of the fundamental constants, are characterized by elegant techniques and novel approaches; and as an example from the field of mass measurement, a definitive experiment at the BIPM ruled out the existence of the so-called 'fifth force'.

As Director of the BIPM, Terry Quinn has been the driving force behind many of the initiatives undertaken in metrology in recent years. As any delegate to conferences or meetings at the BIPM will testify, his knowledge and grasp of complex issues are formidable, abilities that are particularly demonstrated at meetings of the Conférence Générale des Poids et Mesures (CGPM), where many questions of a technical or diplomatic nature are often raised. The signing of the Mutual Recognition Agreement (MRA) at the CGPM in Paris in 1999 by the directors of the NMIs of the industrialized states of the world was largely due to his efforts.

In paying tribute to Terry, it would be remiss not to mention the part played by his charming wife, Renée. She has graciously hosted innumerable functions at the Quinn home over these years and has always made visitors to the BIPM feel most welcome. On behalf of Metrologia, its readers and Editorial Board, I take this opportunity to wish the Quinns a long and happy retirement. At the same time our best wishes go to Terry's successor, Professor Andrew Wallard, another highly honoured metrologist, into whose capable hands the Directorship of the BIPM will pass in January 2004.

Finally, I am delighted to inform readers that starting with Volume 41, the editorial chair will be occupied by Dr Jeffrey Williams. Coming from a distinguished research career in chemical physics and with wide experience in several high-profile posts in the area of publications, Jeffrey is well equipped to expand the horizons of Metrologia in the post-MRA world. With the knowledge that I leave the journal in safe hands, I wish him every success. From my own part, it has been an exhilarating five and a half years spent at the BIPM, a period I shall always look back on with the greatest of pleasure. I take this opportunity to thank my colleagues here at Metrologia, the members of the Editorial Board, reviewers, authors and many friends who have contributed in no small measure to make my stay a most enjoyable one.

This special issue is intended to present a review of mass standards, mass determination and the efforts to replace the international prototype of the kilogram by a new definition of the kilogram based on a fundamental constant of physics.

Mass is a quantity that is familiar to everybody primarily for its importance in commerce. It is not only one of the traditional quantities of metrology but also of science in general. The unit of mass has always been based on a material object and, since 1889, on the international prototype of the kilogram. The mass of any standard weight is derived from this prototype by a cascade of comparison measurements using balances. The sources of uncertainty of the mass of a standard depend upon the circumstances of the weighing process and the long-term instabilities of the intermediate standards. The international prototype—its mass is one kilogram by definition—may also suffer from instabilities or drifts in time, but until now it has not been possible to check this by comparison with a fundamental constant in physics. Repeated verifications of some 40 or so national prototypes of the members of the Metre Convention have shown significant drifts with an average of about 50 µg within 100 years, a fact that casts doubt on the stability of the international prototype itself. Experiments have been underway for about 30 years on linking fundamental constants such as the Avogadro constant or, correspondingly, the atomic mass unit and Planck's constant to the kilogram. Relative uncertainties of the order of 10^-7 have been reached today, still one order of magnitude too large for monitoring the stability of the international prototype or for a new definition.

The first article of this special issue gives information on the international and the national prototypes of the kilogram, its material, manufacture, cleaning procedures, stability investigations and the periodic verifications of national prototypes.

The next article describes methods for determining the mass of multiples and submultiples of the kilogram. In practice, mass standards in the range from one milligram up to several thousands of kilograms are used for the mass determination of commercial objects or for the calibration of weighing instruments. The determination of the mass of multiples and submultiples of the kilogram is a procedure that links such mass standards to the kilogram by a number of—mostly redundant—weighing processes and mathematical procedures that result in the values and the uncertainties of the standards involved.

The reproducibility of E-class weights is the topic of the next article. Classification of weights is defined in an international recommendation for legal metrology and is carried over into the national regulations of most countries. E-class weights are at the highest level in this context. Reproducibility is related to the instability of mass standards within some time interval. Corresponding observations and discussions of the results are reported.

As already mentioned, weighing is an important source of the uncertainty of a mass standard. The requirements on weighing in legal metrology are discussed in the following article. It refers to the project of a new international recommendation for weights (revised OIML R 111) that describes procedures for mass determination and for testing the properties of weights according to the stated requirements for the different classes.

The instability of mass standards is mostly due to surface contamination. A review of the stability of platinum–iridium and stainless-steel standards and their surface contamination is presented in the next article. It gives a comprehensive overview of published data and investigations on this topic.

Magnetic weights interact with the magnetic field generated by a balance. A change in the balance indication is the consequence if certain limits are exceeded. Magnetic properties of weights, their measurements and magnetic interactions between weights and balances constitute the theme of the next article. After an introduction to the theoretical aspects of magnetic fields and magnetic forces, different measurement methods, international comparisons in this field, modelling the interacting forces and finally the impact on the new international recommendation for weights are presented.

The moving-coil Watt balance and the superconducting magnetic levitation experiment are two of the experiments aimed at redefining the kilogram. 'Tracing Planck's constant to the kilogram by electromechanical methods' is the title of the corresponding article. It describes the principles of these experiments and reviews the efforts and results achieved at present in the laboratories concerned.

Another approach to redefining the kilogram is reviewed in the article entitled 'Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal'. This approach is performed in a worldwide collaboration coordinated by the Working Group on the Avogadro Constant of the CIPM Consultative Committee for Mass and related quantities.

An experiment for determining the atomic mass unit by ion accumulation follows a straightforward way for determining the mass of an atom by collecting ions, weighing and 'counting' them by measuring their total charge. This article reports on a 'third' way of redefining the kilogram. This approach is followed by only one laboratory and it is still at an early stage compared with the uncertainties already achieved by the other ones.

The present definition of the unit of mass in the International System (SI) is based on the international prototype of the kilogram, an artefact dating back to the 1880s. At present there is considerable effort worldwide aimed at replacing this artefact definition by one based on physical constants. This paper gives a brief history of the SI unit and how it is currently realized. The focus is on historical information, often forgotten, which has current relevance.

The techniques used for generating multiples and submultiples of the kilogram are reviewed, and their historical evolution is outlined. Emphasis is given to estimation of the values of the measurands, in connection with the need for prior knowledge about them. This need has deep motivation and implies the introduction of constraints on their values. The alternatives of deterministic constraints, leading to the Lagrangian multipliers method, and uncertain constraints, leading to the minimum variance estimator, are discussed, as well as the mathematical relationship between the two methods.

In the uncertainty of E-class weights the need is recognized for an additional component, termed reproducibility, that comes from a time dependence slower than that of the repeatability of the balance but shorter than that of the drifts in mass values that are sometimes seen. The observed scatter over times of the order of one year in the values of check weights is assumed to be due to the repeatability, which is calculable, and the reproducibility which can hence be found by subtraction. Values are given for weights used in this laboratory. The possible origin of this reproducibility uncertainty is discussed and the conclusion reached that it is not related solely to surface phenomena.

A review is given of recent developments in the formulation of requirements of weighing where such measurements are performed in society and industry with legal implications such as safety, fair trade and environmental considerations. Traditional legal metrology in the area of weights and measures has been developed and given an expanded scope in recent years. This reflects, on the one hand, technical and scientific development (computerization of weighing devices, improved weight manufacturing and new methods of magnetism determination, for example), and on the other hand, administrative evolution (global requirements of the market and the Measurement Instrument Directive). Particularly fruitful has been the joint effort by the scientific mass metrology and legal metrology communities in the development in the last decade of international recommendations—especially OIML R111—on weighing. Consensus has been reached in the international weighing forum concerning important areas such as maximum permissible errors for weights, how to calculate measurement uncertainty and how measurement uncertainty should be accounted for in relation to conformity assessment. These international recommendations for weights as mass standards include both tolerances and extensive instructions about various influence quantities that affect the weight result, such as magnetization, surface roughness and volume of weights. Much remains to be done, however: corresponding requirements of weighing devices in particular need to meet the challenges of a rapidly changing technology. The promising collaboration between scientific and legal metrology initiated in the area of weights may act as a model and stimulate similar developments in other areas of metrology, particularly where requirements are generic (for instance uncertainty and conformity) or analogous.

A review of published data on the stability of mass standards has been undertaken. The data mainly focus on the stability of platinum–iridium mass standards, but data on stainless steel artefacts have also been included. The review has been divided into five areas: long-term stability of mass standards, surface effects due to humidity, effects of various cleaning techniques, analysis of surface contamination and the outgassing of surfaces in vacuum. Conclusions have been drawn from the data reviewed, and suggestions for future investigations are proposed.

Unwanted magnetic effects must be minimized and quantified in precision weighing and mass metrology. To this end, methods of measuring magnetic fields and of characterizing the magnetic properties of bodies such as weights are reviewed. The results of comparisons between weights made of ferromagnetic and weakly magnetic materials as well as modelling the magnetic forces between weight and balance are reported. Finally, the impact of the magnetic properties of the weights on regulations in legal metrology is discussed.

Among the priority tasks in the further development of the International System of Units is the redefinition of the kilogram based on fundamental constants. One of the strategies pursued today is to relate mass to Planck's constant h using the equivalence between mechanical and electrical energies. In this paper, possible experimental approaches in this direction are described. The approach which promises to reach the required uncertainty at the earliest is the concept of the moving-coil watt balance. The status of the different watt balance experiments is reviewed in detail.

This paper describes attempts to replace the present definition of the SI unit mass, the kilogram, by a new one, based on the atomic mass unit; the kilogram then becomes the mass of a certain number of silicon atoms. The related research is planned and is to be performed within the scope of a worldwide collaboration coordinated by the Working Group on the Avogadro Constant of the CIPM Consultative Committee for Mass and Related Quantities. This requires determination of the Avogadro constant, N_A, with a relative uncertainty close to 1 × 10⁻⁸. At present, the most important limiting factor is the uncertainty arising from observed differences between some primary density standards as well as the measurement of the molar mass of silicon, e.g. the determination of the natural isotopic composition. Improvements in crystal characterization and density determination are described that allow us to reach a relative uncertainty of about 10⁻⁷. A further reduction in the uncertainty is envisaged by measurements performed on a 99.99% enriched ²⁸Si single crystal.

An experimental approach for linking the atomic mass unit to the kilogram with an uncertainty sufficiently small for a future re-definition of the kilogram is described. The concept consists of accumulation of ions from an ion beam up to a weighable mass and measurable total charge. The main problems and influencing factors connected with ion beam technology, weighing and current measurement together with the corresponding experimental solutions are discussed in detail. The first experiments with consistent results, but still large uncertainty, are described.

The PDF file provided contains web links to all articles in this volume.